# Warp elements of a univariate functional dataset

### Description

This function carries out the warping of elements of a univariate functional dataset by using a set of pre-computed warping functions.

### Usage

1 |

### Arguments

`fData` |
the functional dataset whose observations must be warped in
form of |

`warpings` |
the warping functions |

### Details

Given a univariate functional dataset *X_1(t), …, X_N(t)* and a set
of warping functions *H_1(t), …, H_N(t)*, such that:

* H_i : s \longrightarrow t = H_i(s), \quad \forall i = 1, …, N,*

where *s* spans the warped (or registered) grid and *t* spans the
original grid, the function computes the warping given by the following
composition:

* X_1 \circ H_1(t), …, X_N \circ H_N(t).*

### Value

The function returns the univariate functional dataset of warped
functions, in form of `fData`

object.

### See Also

`fData`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | ```
set.seed( 1618033 )
N = 30
t0 = 0
t1 = 1
P = 1e3 + 1
time_grid = seq( t0, t1, length.out = P )
means = round( runif( N,
t0 + (t1 - t0) / 8,
t1 - (t1 - t0) / 8 ), 3 )
Data = matrix( sapply( means,
function( m )( dnorm( time_grid, mean = m, sd = 0.05 ) ) ),
ncol = P, nrow = N, byrow = TRUE )
fD = fData( time_grid, Data )
# Piecewise linear warpings
template_warping = function( m )( c( time_grid[ time_grid <= 0.5 ] * m / 0.5,
( time_grid[ time_grid > 0.5 ]
- 0.5 ) * (1 - m ) / 0.5 + m ) )
warpings = matrix( sapply( means, template_warping ),
ncol = P,
nrow = N, byrow = TRUE )
wfD = fData( time_grid, warpings )
fD_warped = warp( fD, wfD )
dev.new()
par( mfrow = c( 1, 3 ) )
plot( fD,
main = 'Unregistered functions', xlab = 'actual grid', ylab = 'values' )
plot( wfD,
main = 'Warping functions', xlab = 'registered grid',
ylab = 'actual grid' )
plot( fD_warped,
main = 'Warped functions', xlab = 'registered grid',
ylab = 'values' )
``` |

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